STATUS OF IGS ORBIT MODELING & AREAS FOR IMPROVEMENT

1. Earth radiation pressure (albedo) accelerations • see posters by C. Rodriguez Solano et al. (this afternoon) • Spurious rotations & translations in AC solutions • compare Rapid & Finals daily orbits • check indirect AC orbit effects on polar motion, LOD, geocenter • study discontinuities between daily orbits • Inconsistent AC yaw-attitude models • mostly affects clock estimates during eclipse season STATUS OF IGS ORBIT MODELING & AREAS FOR IMPROVEMENT Jim Ray & Jake Griffiths NOAA/National Geodetic Survey EGU 2011, Session G2.4, Vienna, 8 April 2011

2. Approaches to Study Orbit Errors • SLR ranging is only direct, independent method • but just 2 old GPS Block IIA SVs with retro-reflectors (PRNs 05 & 06) • PRN05 was decommissioned in 2009 • results suggest neglect of albedo shifts orbit origin few cm away from sun • not considered here → see posters by C. Rodriguez Solano et al. • Or, can check indirect effects on polar motion, LOD, & geocenter estimates • net constellation rotations about RX & RY should ideally match polar motion offsets in PMy & PMx • LOD changes are indistinguishable from –dRZ/dt, net rate of satellite Right Ascensions (axial rotation rate) • compare LOD to independent multi-technique UT1+LOD combinations • compare geocenter motion to SLR & load models • Can also study discontinuities between daily orbits at ~24:00 • samples 1 point in orbit per day • aliases any subdailyharmonic orbit errors into longer-period features (except S1 & S2) 02

3. Compare 3 years of daily orbits: 1 Jan 2008 to 31 Dec 2010 • Net daily constellation rotations are a leading orbit error • must come mostly from modeling of satellite dynamics • note non-zero RY mean bias • Implies short-period orbit precision > 8.2/√2 ≈ 5.8 mm • this is 1D lower-limit estimate => 3D precision is >10.1 mm • common-mode errors (e.g., subdaily EOP tide model) not visible here • Other common-mode IGR/IGS errors also not visible here • long-period (> 1 d) errors • e.g., due to Reference Frame or analytical form of empirical orbit model 03

4. Spectra of (Rapid-Final) Orbit Rotation Differences greater RZ power in weekly band probably related to weekly UT1 updates in AC Finals • Rotation differences nearly featureless • except for background of flicker noise down to sub-weekly periods (1096 d from 1 Jan. 2008 – 31 Dec. 2010) 04

5. AC Orbit & Polar Motion Consistency • A constant rotational shift of TRF, e.g., should offset orbit frame & polar motion (PM) equally • expect: orbit RX ≈ ΔPMy & orbit RY ≈ ΔPMx • But, a net diurnal sinusoidal wobble of orbit frame will alias entirely into a PM bias • does not equal any net rotational offset of orbit frame • Likewise, prograde diurnal PM errors can alias into empirical once-per-rev (12-hr) orbit parameters • e.g., due to errors in ~24-hr terms of subdaily EOP tide model • net impact on orbit frame depends on geometry of orbit planes & SRP model terms • So, check of orbit frame vs PM rotational consistency can provide insights into AC analysis weaknesses • note, though, that most ACs apply some over-constraints on orbit and/or PM variations (only ESA & NGS claim none; CODE has strongest)

6. Rotational Self-Consistency of IGS Final Orbits/PM ESA GFZ • Orbit rotations more variable than PM residuals for all ACs COD MIT JPL NGS

7. AC Orbit Modeling Differences • Most ACs use CODE Extended Orbit Model in some form, with empirical SRP parameters adjusted deterministically • COD: D,Y,B scales + 1/rev in B + 12-hr velocity brks w/ constraints • ESA: D,Y,B scales + 1/rev in B + along-track offset & 1/rev • GFZ: D,Y,B scales + 1/rev in B + noon velocity brks • GRG: D,Y scales + 1/rev in D,B + velocity brks in eclipse • MIT: D,Y,B scales + 1/rev in D,Y,B w/ constraints • NGS: D,Y,B scales + 1/rev in B + noon velocity brks • SIO: D,Y,B scales + 1/rev in D,Y,B w/ constraints • (frames oriented toward the Sun) • Except 2 ACs that use frame oriented toward the Earth with stochastic SRP estimation • EMR: X,Y,Z scales + stochastic X,Y,Z • JPL: X,Y,Z scales + stochastic X,Y,Z • Geocenter & LOD estimates (among others) known to be sensitive to solar radiation pressure modeling • especially Y & Z components of geocenter 05

8. IGS Final LOD Residuals (AC – JPL KEOF) • Strong harmonic modulations visible for all ACs • but amplitudes vary among ACs 06

9. Spectra of AC LOD Differences • Aliased subdaily UT1 errors, semi-annual, & 6th GPS draconitic aliased sub-daily UT1 tide errors 6th GPS draconitic 07

10. Spectrum of IGS Rapid Combined LOD Differences (1024 d from 2 May 2008 – 19 Feb. 2010) • IGS combination “calibrates” AC LOD biases by comparison with IERS Bulletin A over a 21-d sliding window • process seems effective at mitigating most LOD flicker & long-period noise

11. Draconitics in AC Reprocessed LOD Differences ~14-d band • Amplitude spectra from reprocessed years 1994/1998 - 2007 • level of draconitics highly variable among ACs (but over long spans) draconitics (from P. Rebischung, 2011)

12. Compare Geocenter Z Variations • IGS & JPL results from reprocessing + operations since 2007 • out of phase with each other since ~2008.5 completely out of phase afterwards 08

13. Compare Geocenter Z Variations • ILRS results (from ITRF2008) mostly out of phase with IGS/JPL before ~2004.5 • IGS/JPL both show persistent bias started becoming more phase coherent 09

14. Compare Geocenter Z Variations • JPL Z geocenter more in phase with load model since ~2008 • recent IGS results are completely out of phase • may suggest recent JPL orbit modeling is better but amps are large JPL more in phase with load model than is IGS 10

15. Compare Geocenter X Variations • IGS & JPL agreement generally similar for X geocenter • but IGS better at some times (e.g., 1999-2000 &2003-2004) • long-term GNSS X origin less stable than ILRS or load model

16. Compare Geocenter Y Variations • IGS results strongly skewed before ~1998 for Y geocenter • both IGS & JPL poorly centered over most of span • probably mostly related to solar radiation pressure modeling

17. Compute Orbit Discontinuities • Fit orbits for each day with BERNE (6+9) orbit model • fit 96 SP3 orbit positions for each SV as pseudo-observations for Day A • parameterize fit as plus 3 SRPs per SV component • propagate fit forward to 23:52:30 for Day A • repeat for Day B & propagate backwards to 23:52:30 of day before • Compute A,C,R orbit differences at 23:52:30 • Use 2049 d from 23 May 2005 thru 31 Dec 2010 • spectra for all SVs stacked for each AC; data gaps linearly interpolated • sliding boxcar filter used to smooth across each 3 adjacent frequencies • previous procedures have been refined for improved results • Power of fit/extrapolation error “calibrated” using similar test for observed values at 23:45 11

18. Spectra of IGS Orbit A,C,R Discontinuities possible aliased sub-daily EOP tide errors ? • Strong peaks near same subdaily EOP alias lines as LOD spectra • but frequencies do not exactly match aliases for 24-hr sampling • also effects differ for each A,C,R component • 3rd GPS harmonic important in cross-track & radial components 3rd GPS draconitic 12

19. Simulate Orbit Errors from Subdaily EOP Model SVN34/PRN04 sample daily @ 23:45 • Compare NGS orbits using IERS & test subdaily EOP model • for test EOP model, change tidal admittances by ~20% • sample daily differences at 23:45 & convert to A,C,R frame • subdaily periodic differences will alias to longer periods in spectra 13

20. Spectra of Simulated A,C,R Subdaily EOP Errors sub-daily EOP tide errors alias differently for orbits • Coupling of subdaily EOP errors into orbit parameters is complex • normal ~7, ~9, ~14, & ~29 d alias lines are split & frequency shifted • apparent draconitic features created, especially 3rd harmonic • large annual (K1 alias ?) signal but little semi-annual power 3rd + other GPS draconitics created 14

21. Impact of AC Yaw-Attitude Models on GPS Clocks 3 cm PRN03/SVN33 (IIA – 1996) • Diverse AC models for yaw-attitude variations during eclipse cause large clock discrepancies for older Block IIA GPS satellites • some ACs get rejected from clock combination • Must adopt a common yaw model for ACs & PPP users (ESA is clock reference) 15

22. Summary & Conclusions • Rotational variations are a leading IGS orbit error • background spectrum shows flicker noise • probably is main source of flicker noise in station position time series • Larger variations in AC orbit frame rotations than polar motion • cause is unclear but must be related to AC analysis methods • could be affected by a prioriAC constraints • LODs show clear aliasing of subdaily EOP errors + 6thdraconitic + semi-annual • Orbit discontinuities at day-boundaries reveal error details • subdaily EOP tide errors alias very strongly into orbit parameters, especially in cross-track • but alias frequencies shifted & split compared to 1d sampling • annual or K1 tide alias errors important in along-track • 3rd & other draconitic harmonics created by subdaily EOP errors • Adoption of common model for yaw variations is mandatory • otherwise combined SV clocks during eclipse are degraded 16